Singularity of a matrix

A matrix is singular if it does not have an inverse, meaning there's no single matrix that, when multiplied with it, results in an identity matrix (like 1 in regular numbers). In practical terms, a singular matrix represents a system of equations with either no solutions or infinitely many solutions, often indicating that some equations are redundant or dependent. This happens when the matrix's determinant (a special number calculated from it) equals zero. So, a singular matrix fails to be invertible because it lacks the necessary properties for unique solutions.